How to use
Enter each independent group’s mean, standard deviation and sample size. Means may be negative; standard deviations must be positive and both sample sizes must be whole numbers of at least two. Keep the measurement unit and outcome definition identical across groups.
The pale example compares means 12 and 10 with standard deviations 3 and 4 and sample sizes 20 and 30. It can be calculated immediately. Focusing any numeric field clears all six examples once; later edits keep your values. Any edit invalidates the confirmed result and Copy result stays disabled until a new calculation.
Calculation and result fields
The pooled standard deviation is sqrt([ (n₁−1)s₁² + (n₂−1)s₂² ] / [n₁+n₂−2]). Cohen's d is (mean₁−mean₂)/pooled SD. It is unitless because the difference is scaled by within-group variability. The page reports the signed value: a positive sign means group 1 has the higher mean, and exchanging the groups reverses the sign.
Hedges' g uses the common approximation J = 1 − 3/[4(n₁+n₂−2)−1], then g = Jd. This reduces small-sample bias but is still an approximation. The result cells also show the raw mean difference, pooled SD and correction factor so the direction and scale can be checked.
Worked examples
For means 12 and 10, SDs 3 and 4, and n values 20 and 30, pooled SD is about 3.63. Cohen’s d is about 0.55 and approximate Hedges’ g is about 0.54. Swapping every group input gives −0.55 and −0.54 while keeping their magnitudes.
If both means are 5, with positive SDs, the difference, d and g are zero. A zero effect size describes equal sample means relative to the pooled SD; it does not prove that the population means are identical.
Interpretation and appropriate use
Effect size helps describe a standardized difference when two measurements use the same construct but raw units alone are hard to compare. Report the sign, raw difference, confidence interval from an appropriate method, sample design and subject-matter context.
Rules such as 0.2 small, 0.5 medium and 0.8 large are rough conventions, not universal decision thresholds. A value important in medicine may differ from one important in education or operations. A large magnitude does not establish causality, benefit, statistical significance or acceptable risk.
Limits and common errors
This page uses the pooled-variance form for two independent groups. It does not test equality of variances, calculate Welch statistics, paired-sample effects, p-values, confidence intervals or power. For repeated measurements, matched participants or unequal-outcome definitions, use a method designed for that study.
Standard deviation must not be zero because d would have a zero denominator. Sample SDs should be computed consistently. Very skewed data, outliers, ordinal scales and tiny samples can make a mean-and-SD summary misleading. Rounding is for display; the calculations retain precision.
Common questions
Why do n values matter? They determine the weights in the pooled SD and the Hedges correction. Why can d be negative? Direction is preserved as group 1 minus group 2. Is g always smaller? With valid finite samples this approximation has a correction below one, so its magnitude is slightly smaller.
Can this choose a treatment or business action? No. Combine the estimate with uncertainty, study quality, costs, harms and domain thresholds. Copy result exports the displayed statistics as text but does not save or transmit inputs.